Spring-constant

Spring-constant

I don't know where it came from but an old formula based on empiric data states the following.

k = P/(0.0075 x d)

P = Vertical load on pile (f.e. kN)d = Ø of the pile (f.e. m)

Another way to determine the spring constant is by using Hook's law. Be careful with this formula because in reality you will have different (lower) values. To compensate this you should also calculate the vertical differential soil movement for the additional deformation. This additional deformation will be a lot bigger than the one comming out of Hooks law.

Equitation for the springconstant k:

1/k = 1/kp + 1/ks

Spring equitation for the pile:

F = -kp . xorkp = - F / x

kp = spring constant for the pile  ( f.e. kN/m )  x = deformation      ( f.e. m )F = resulting force   ( f.e. kN )

Hook's Law

σ = E . ε

and

σ = F / A

→ E . ε = F / A

→ E . Δl / L = F / A

→ E . Δl / L = k . Δl  / A

→ kp = E . A / L

Spring-constant general

kp = E x A / L

A = Surface of section (f.e. m²)E = Elastic Module (f.e. kN/m²)L = Length of the element (f.e. m)

Spring equitation for the soil:

ks = 80 D . qp         for round pilesks = 90 b . qp         for square piles

D = Ø of the pile (f.e. m)b = width of the square pile (f.e. m)qp = is the bearing resitance value at the bottom of the pile (f.e. kN/m²)